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A Lucas chain for an integer n>=1 is an increasing sequence 1=a_0<a_1<a_2<...<a_r=n of integers such that every a_k, k>=1, can be written as a sum a_k=a_i+a_j of smaller ...

A matrix for which horizontal and vertical dimensions are the same (i.e., an n×n matrix). A matrix m may be tested to determine if it is square in Wolfram Language using ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

The identity F_n^4-F_(n-2)F_(n-1)F_(n+1)F_(n+2)=1, where F_n is a Fibonacci number.

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

The harmonic mean H(x_1,...,x_n) of n numbers x_i (where i=1, ..., n) is the number H defined by 1/H=1/nsum_(i=1)^n1/(x_i). (1) The harmonic mean of a list of numbers may be ...

Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...